Extension of multi-commodity closed-loop supply chain ...Extension of multi-commodity closed-loop...

ORIGINAL PAPER

Extension of multi-commodity closed-loop supply chain networkdesign by aggregate production planning

Leena Steinke1 • Kathrin Fischer1

Received: 30 June 2015 / Accepted: 17 October 2016 / Published online: 14 November 2016

� The Author(s) 2016. This article is published with open access at Springerlink.com

Abstract In this work the influence of production and

capacity planning on decisions regarding facility location,

distribution quantities and component remanufacturing

(and vice versa) in a closed-loop supply chain network

(CLSCN) with multiple make-to-order products is studied.

A mathematical model, the facility location, capacity and

aggregate production planning with remanufacturing

(FLCAPPR) model, for designing the CLSCN, for planning

capacities at the facilities and for structuring the production

and distribution system of the network cost-optimally, is

formulated. It consists of a facility location model with

component remanufacturing over multiple time periods,

which is extended by capacity and production planning on

an aggregate level. The problem is solved for an example

set of data which is based on previous CLSC research in

the copier industry. In a numerical study the effect of the

extended planning approach on the decision to process

returned products is determined. Furthermore, the

FLCAPPR model is solved for different returned product

quantities and numbers of periods in the planning horizon

to study the influence on the network design and on the

procuring, production and distribution quantities. It turns

out that decisions regarding the locations of and the

capacity equipment at facilities and decisions regarding the

production and distribution system are interdependent;

therefore, they have to be managed jointly. Furthermore, it

is shown that the decision to process returned products and

use remanufactured components in the production does

depend not only on the costs, but also on the quantity of

returned products and the length of the planning horizon.

Keywords Closed-loop supply chain management �Network design � Remanufacturing � Reverse logistics �Aggregate production planning � Capacity planning

1 Introduction

Supply chains with product recovery differ, depending on

the characteristics of the product, the recovery activity

which is used and whether this activity is done by the

original equipment manufacturer or a third party [6]. In

general, supply chains with product recovery can be dis-

tinguished into open-loop and closed-loop supply chains

(CLSC). If there is hardly any connection of the forward

and return product flows, the supply chain is open-loop and

the forward and reverse product flows are managed sepa-

rately. The forward product flow can be described by the

traditional supply chain management theory, and the

reverse product flow is planned independently by reverse

supply chain management [25]. If the forward and return

product flows are related, e.g. customers supply their used

products as production inputs, the supply chain is closed-

loop. In this case, often an integrated management of both

flows is necessary to achieve an optimized CLSC; for

further details see [8, 9].

In this work, a supply chain is studied which is closed by

component remanufacturing. Remanufacturing is also

This article is part of a focus collection on ‘‘Robust Manufacturing

Control: Robustness and Resilience in Global Manufacturing

Networks’’.

& Leena Steinke

[email protected]

Kathrin Fischer

[email protected]

1 Institute of Operations Research and Information Systems,

Hamburg University of Technology, Schwarzenbergstr. 95,

21073 Hamburg, Germany

123

Logist. Res. (2016) 9:24

DOI 10.1007/s12159-016-0149-4

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called value-added recovery, since it describes a series of

operations which restore the value of a product after usage

[11]. A supply chain with remanufacturing is extended by

the following activities: collecting, cleaning and testing

returned products. Then, remanufacturable products are

disassembled into components, which are remanufactured,

e.g. repaired or refurbished. After testing these compo-

nents, they are reassembled and sold in secondary markets

as remanufactured items or reintegrated to the original

supply chain and used as as-new items [11], as in the

supply chain studied in this work. High-value products, e.g.

copiers and automobiles, are suitable for component

remanufacturing. A further discussion of product charac-

teristics that enable remanufacturing can be found in [18].

Whether the supply chain is open- or closed-loop, pro-

duct recovery forces supply chain management (SCM) to

consider a reverse product flow. In addition to the planning,

realization and control of all operations, production,

inventory and distribution quantities and information flows

from the product origin to the point of consumption, all

problems concerning the way back through the supply

chain, i.e. after consumption, have to be considered in a

SCM with product recovery. These decision problems can

be differentiated regarding their planning horizon: some

are made on a yearly basis and determine the framework

for decisions, which are made on a weekly or monthly basis

[26]. Then again, these decisions constrain the operational

decisions, which occur every day [20].

The network design, decisions regarding the product and

material programme, supplier selection, collection strategy,

take-back arrangements and supply chain coordination are

strategic decision problems and belong to long-term plan-

ning. Decision problems regarding inventory management

and production planning are tactical and have a mid-term

planning horizon. Operative decision problems, as disas-

sembly planning, material requirement plans, scheduling

and routing in the remanufacturing shop have a short-term

planning horizon [4, 5, 7, 28].

In order to achieve an optimized CLSC the tactical

planning has to be considered by strategic management

[14, 21, 26]. Long-range forecasts of aggregate product

demand are the input for strategic planning [5]. They are

used by the mathematical model developed in this work to

derive a cost-optimally network design, i.e. cost-optimal

facility locations and capacity equipment, with cost-opti-

mal procuring, transportation, production and storage

quantities. The quantities are planned on an aggregate

level; therefore, fluctuations of data are neglected and the

modelling approach is deterministic.

In the facility location problem (FLP), facilities are

located and quantities of goods are allocated and dis-

tributed in the network a cost-optimal way, e.g. in [2]. In

the special case of a CLSN with reverse product flows

these models support the procuring decision, i.e. when to

recover returned products and use them as production

inputs, as well, e.g. in [8, 9].

In the literature so far, location/allocation models in a

CLSCN consider opening costs of product recovery facil-

ities, but costs for volume capacity and costs for installing

technology or hiring workforce for the operations at the

respective facilities of the network, especially for product

recovery operations, are neglected. However, to determine

a cost-optimal procurement policy, i.e. to decide when to

recover returned products and use the resulting items as

production inputs instead of new items procured from

suppliers, these costs have to be included.

Since remanufacturing is a labour-intensive operation

(see [13] for an extended discussion), labour hour costs are

relevant for the decision to process returned products. The

well-established aggregate production planning (APP)-

framework is used to plan the production and workforce at

facilities cost-optimally in this work. In APP, the length of

the planning horizon is usually between 6 and 24 months

[3] and quantities are planned on an aggregate level. In the

following this APP-approach is described and a multi-pe-

riod facility location problem extended by capacity and

aggregate production planning is developed.

The consideration of different product compositions,

component remanufacturing and component commonality

is possible with this modelling approach, and the influence

of different return rates can be investigated. Hence, dif-

ferent realistic SC settings can be captured.

The rest of the paper is organized as follows: relevant

selected literature regarding network design and aggregate

production planning is presented and discussed in the next

section. Here, the differences between other contributions

and the approach taken in this work are also discussed. The

CLSCN and the production planning problem are presented

in detail in Sect. 3. Afterwards the planning problem is

described mathematically in Sect. 4. In Sect. 5, it is solved

for an example data set and the results are presented.

Furthermore, a sensitivity analysis is performed and

selected results are discussed in Sect. 5, too. Finally, con-

clusions and possibilities for further research are stated.

2 Literature review

Networks with product recovery are mathematically opti-

mized by extending the classical Warehouse Location

Problem (WLP) to capture reverse product flows. Mostly

these problems are described by Mixed Integer Program-

ming (MIP) and Mixed Integer Linear Programming

(MILP) models. In the following, selected papers are dis-

cussed, which present the state of research, and have

influenced this study. A more detailed review of network

24 of 23 Logist. Res. (2016) 9:24

123

design literature concerning supply chains with product

recovery is offered in [1].

As one of the first, Marin and Pelegrin [19] study a

network with reverse product flows: customers get products

at plants and return them to plants. The objective is to find

the optimal plant location and shipping quantities, such that

the costs for opening facilities and for transportation are

minimized. Marin and Pelegrin’s [19] model is an unca-

pacitated Facility Location Problem (FLP), whereas the

other models discussed in the following are capacitated

FLP.

Following [19], in this work it is assumed that customers

return their products to those facilities from which the

products are distributed. Unlike [19], in the network stud-

ied here, these facilities are not plants, but facilities for

distribution and collection of products, called distribution

and collection centres (DCCs). Furthermore, in [19] a

single product type is considered, whereas in this work

multiple product types are studied.

A remanufacturing network with multiple product types

is examined by Jayaraman et al. [15]. Used products are

shipped from collection zones to remanufacturing centres,

where they can be remanufactured or stored. Remanufac-

tured products are distributed, i.e. are used to fulfil cus-

tomer demand, or stored. The shipping quantities between

collection zones, customers and remanufacturing/distribu-

tion locations are to be determined optimally; the objective

is cost minimization.

In this work, following [15], it is assumed that returned

products can be stored at remanufacturing centres. As in

[15], the storage capacity at remanufacturing facilities is

assumed to be limited. Additional to storage capacities,

capacities for operations at facilities are planned in this

work, too.

Operative capacity equipment is studied by Schultmann

et al. [24]. The model by [24] allocates the optimal operative

capacity equipment to open facilities of an existing reverse

supply chain. The capacity at facilities is needed for opera-

tions, as e.g. inspection and sorting, of multiple product

types. The objective is to minimize costs, caused by capacity

equipment, production and distribution quantities.

Unlike in [24], in this work a closed-loop system is

studied, i.e. in addition to reverse product flows, forward

product flows are considered. Fleischmann et al. [8] and

Fleischmann et al. [9] study such a closed-loop system as a

three echelon network, consisting of warehouses, plants

and test centres, where products are recovered. These

facilities have to be located optimally, and the quantities of

the forward and reverse product flows of the network are to

be determined such that costs for opening, transport and for

unsatisfied demand and not-collected returned products are

minimized under capacity limitations for the product flows

between facilities of different network echelons.

Salema et al. [23] extend the model from [9] to study

multiple product types. Furthermore, in [23] the product

flow capacity at facilities is limited by maximum and

minimum capacity bounds for the facilities.

As in [9, 23], the CLSCN studied in this work has three

facility levels. Here, the three facility levels of the CLSCN

are DCCs, plants and suppliers and remanufacturing cen-

tres, both delivering components to plants. The production

system of the CLSCN consists of two stages: at the first

stage components are delivered from remanufacturing

centres or from suppliers to plants, where they are assem-

bled to products. This way, component remanufacturing,

unlike product remanufacturing as in [9, 15, 19, 23], with

different product and component types and component

commonality in the assembly of different product types can

be modelled.

In contrast to [9, 15, 23], the capacity for storage and

product and component flows at facilities are decision

variables, i.e. have to be determined out of a parameter

range and induce costs. In addition, capacity for the oper-

ations at facilities is determined by the model stated in this

work. Hence, the influence of different capacity types on

the facility location decisions and on the decision to pro-

duce, remanufacture, store or distribute is studied.

All studies discussed above have a single time period

planning horizon. Following [15, 21] consider inventory in

a single time period planning facility location problem and

study the trade-off between storing and distributing prod-

ucts. Further discussions of inventory in distribution net-

works and the interdependence of inventory, transportation

and facility location can be found in [21] and different

approaches to extend facility location problems by inven-

tory management can be found in [26].

In this work, the planning horizon of the CLSCN design

problem is modified to a multi-period setting, as in [22] and

[30]. Pishvaee and Torabi [22] use a multi-objective

approach to combine cost minimization of the CLSCN with

the minimization of delivery tardiness for the single pro-

duct case. In this work, the objective is to minimize costs

and the production and capacity planning problem at open

facilities in a network with multiple commodities is con-

sidered in a MILP-approach.

In this work, a FLP for a closed-loop supply chain with

component remanufacturing is extended by production

planning on an aggregate level, using the idea of APP, as in

Steinke and Fischer [30]. In APPs, the different products

are aggregated to product types and the capacities are not

product specific, but are summarized and stated in common

units, e.g. labour hours. APP is used to determine cost-

optimal manufacturing and storage plans, which match the

limited means in terms of workforce or working stations,

respectively, and production input with forecasted demand

[20]. The planning horizon of an APP can vary; usually it

Logist. Res. (2016) 9:24 of 23 24

123

consists of 6–24 months, [3]. In particular, when adjust-

ments of capacities are allowed in each period, the periods

have to be sufficiently long.

Jayaraman [16] studies the production planning problem

of a company, which offers recovered mobile phones for a

secondary market. He states the Remanufacturing APP

(RAPP) model, which minimizes costs by determining the

optimal disassembly, disposal, remanufacturing, procure-

ment and storage quantities under fixed workforce

capacities.

In this work, the approach of [16] is followed to model

the production system. While in [16] the reverse product

flow is managed, here, a closed-loop system is studied, and

the model is extended accordingly, i.e. the remanufactured

components are reintegrated into the original supply chain

instead of being shipped to secondary markets. Moreover,

in contrast to [16], capacities in volume units and labour

hours at facilities are not fixed but can be adjusted over the

planning horizon.

In the RAPP proposed by [16] only one site for

remanufacturing is considered, whereas in this work,

multiple possible facility locations exist. Hence, the APP

for a closed-loop system is integrated into a FLP.

Extending a yearly FLP for a CLSCN with component

recovery by an APP on a monthly basis leads to a model

with extensive solution times. Furthermore, the considered

capacities cannot be adjusted within one month; especially,

decisions regarding the volume capacity are made on a

strategic level. Therefore, also the APP is extended and the

APP is modelled for a strategic, yearly, planning horizon.

With such an extended strategic planning model, deci-

sions regarding the location of facilities and their capacity

equipment for operations and storage can be studied

jointly. Furthermore, different product and component

types are considered and the interdependence of process-

ing, storing and distributing them is examined. Moreover,

by considering capacity costs and operative capacity in

addition to storage capacity, the cost effects of the deci-

sions regarding the returned products, i.e. if they are

remanufactured, stored or disposed, are captured com-

pletely unlike in facility location problems without

capacity and production planning.

Following [9, 19, 23, 30], a fixed relation between

demand and returned products is assumed in this work; the

returned product quantity is determined as a fraction of the

sold product quantity. As in [30], the CLSCN is studied

over multiple time periods, and hence, there is a time lag

between the selling and the returning of a product. In [30] it

is assumed that products are returned by customers after

one period of usage. However, products can stay longer

with the customers, i.e. the residence time of a product,

defined as the number of periods a product is used by a

customer, can be longer. Furthermore, products are

returned not only in a specific period following the buying,

but in all subsequent periods of the planning horizon. In

this work, the model in [30] is extended to capture these

aspects.

Moreover, the FLCAPPR model developed in this work

determines cost-optimal volume capacities and optimal

workforce size at the facilities for every period. In contrast,

in [31] the capacity planning is integrated in a more sim-

plified way, such that overcapacities can occur: whenever a

facility is opened, its volume capacity and workforce are

set to their respective upper limits and adjusted to the

actual required levels only in the last period. Furthermore,

while in [30] total costs are minimized, here discounting is

considered in the objective function, too.

3 Problem description

In this section the network structure of the CLSCN with

component remanufacturing is introduced and the respec-

tive planning problem is described in detail.

The CLSCN consists of nodes, which represent cus-

tomers and facilities with their operations, and arrows,

which show the flows of multiple commodities through the

network, see Fig. 1. There are five different types of nodes:

costumers, DCCs, remanufacturing centres, plants and

suppliers. Customers demand different product quantities

in each period, and they return their products to DCCs in a

later period, i.e. it is assumed that a known fraction of

products shipped to customers in one period is returned in a

later period of the planning horizon. The residence time of

products can be different, but there is a given number of

periods the product has to stay with a customer before it is

returned and considered as remanufacturable. The mini-

mum residence time can be interpreted as the minimum

number of periods a product is in full working condition.

Demand quantities are assumed as deterministic and

known; therefore, the returned product quantities are

deterministic and known, too. Demand is lost whenever it

is not met, i.e. it cannot be backlogged.

The CLSCN consists of three facility levels: DCCs,

plants, remanufacturing centres and suppliers. The latter

are summarized to one level since both provide compo-

nents. Supplier locations are given, whereas the locations

of DCCs, remanufacturing centres and plants have to be

determined. These facilities can be opened in one period

and then remain open or are closed in a later period. It is

assumed that once a facility is closed, it cannot be opened

again.

Capacities at facilities are determined in volume and

labour hours. The volume capacity restricts the volume of

commodity flows passing a facility and, if existent, the

volume of stocked products and components, respectively.

24 of 23 Logist. Res. (2016) 9:24

123

The labour hour capacity limits the available hours of the

workforce needed for remanufacturing and assembly at

remanufacturing centres and plants, and for handling

products at DCCs.

Capacity levels at facilities are determined once a

facility is opened and can be adjusted in a later period, i.e.

they can be expanded or reduced in fixed steps in every

period.

The product and component flows through the network

are described by three different types of arrows, see Fig. 1.

The solid arrows show the forward product flows, which

are shipped from plants to DCCs and further to the cus-

tomer locations. The dotted arrows describe the component

flows leaving suppliers or remanufacturing centres,

respectively, to plants. The dashed arrows represent the

reverse product flows, i.e. the flows from customers to

DCCs and from DCCs to remanufacturing centres. In this

CLSCN redistribution is possible, i.e. products and com-

ponents can be shipped between facilities of the same type.

DCCs are bi-directional facilities, because products flow

through DCCs to customers and customers return used

products to DCCs. At DCCs returned products are col-

lected, visually inspected and, afterwards, they are shipped

either to remanufacturing centres or to the disposal unit.

The decomposition of returned products into compo-

nents and the remanufacturing of those components to an

as-new condition is performed at remanufacturing centres.

It is assumed that components can be remanufactured

repeatedly in the planning horizon, i.e. the limited number

of possible remanufacturing cycles for components is not

reached. However, there is a known and constant fraction

of components that cannot be remanufactured to the quality

standards of as-new components with a reasonable given

effort and therefore has to be disposed. Moreover, at

remanufacturing centres it is possible to store returned

products, instead of remanufacturing them immediately.

At plants, components are assembled to products of

different types. Product types differ regarding their com-

bination of components, i.e. at least one component in the

product composition has to be different in different prod-

ucts. Components can be product type-specifically or

commonly used among different product types. They are

shipped from suppliers or remanufacturing centres to plants

and can be held on inventory at plants. No final products

are stored in the studied network and products are assem-

bled only if an order exists (MTO). Since the planning

horizon is strategic, no lead-times for operations or trans-

port are considered.

For each planning period the demand and return product

quantities are known, while facility locations and capacity

equipment at the facilities, as well as procurement, trans-

portation, production and inventory quantities, have to be

determined with the objective of total cost minimization.

To support these decisions, the planning problem is for-

mulated as a MILP, presented in the next section.

4 The facility location, capacity and aggregateproduction planning with remanufacturingproblem

In this section, the planning problem described above, the

Facility Location, Capacity and Aggregate Production

Planning with Remanufacturing (FLCAPPR) Problem, is

stated and explained using the notation listed in Tables 1, 2

and 3, presented below. The model presented here is an

extension of the model given in [30], as described in Sect. 2

above.

Fig. 1 Closed-loop supply chain network

Logist. Res. (2016) 9:24 of 23 24

123

The objective function of the FLCAPPR problem mini-

mizes the discounted total costs of the CLSCN over multiple

time periods. As the model combines multi-period facility

location, capacity and aggregate production planning, the

objective function consists of cost terms for opening, running

and closing facilities, for the volume capacity equipment and

the labour force at open facilities, for processing and storing

goods at facilities, for procuring components at suppliers, for

transporting goods in the network and for disposing returned

products and components.

Table 1 Definition of relevant

setsSet Definition

C Set of components, c 2 C

F Set of potential plants, f 2 F

FD F [ Df g, set of potential plants and the disposal unit D

K Set of customer locations, k 2 K

P Set of products, p 2 P

R Set of potential remanufacturing centres, r 2 R

RD R [ Df g, set of potential remanufacturing centres and the disposal unit D

T Set of time periods, t 2 T

V Set of potential DCCs, v 2 V

Z Set of suppliers for components, z 2 Z

Table 2 Definition of relevant variables

Variable Definition

Capyt Number of capacity steps at open facility y in period t (in m3), 8y 2 F [ V [ R; t 2 T

CCapyt Expansion or reduction of capacity steps at facility y in period t (in m3), 8y 2 F [ V [ R; t 2 T

CCapDyt Reduction of capacity steps at facility y in period t (in m3), 8y 2 F [ V [ R; t 2 T

CCapUyt Expansion of capacity steps at facility y in period t (in m3), 8y 2 F [ V [ R; t 2 T

EIfc Quantity of c remaining in the inventory of plant f at the end of the last planning period, 8f 2 F; c 2 C

EIrx Quantity of x remaining in the inventory of remanufacturing centre r at the end of the last planning period,

8r 2 R; x 2 C [ P

EXIywxt Quantity of x transported from facility y to facility w of the same echelon in period t,

8y;w 2 F [ V [ R : y 6¼ w; x 2 C [ P; t 2 T

Hyt 1; if facility y is closed in period t

8y 2 F [ V [ R; t 2 T

0; otherwise

8<

:

Ifct

Quantity of c remaining at plant f at the end of period t, 8f 2 F; c 2 C; t 2 T

Irxt Quantity of x remaining at remanufacturing centre r at the end of period t, 8r 2 R; x 2 C [ P; t 2 T

LCapyt Workforce available at facility y in period t, 8y 2 F [ V [ R; t 2 T

Ukpt

Number of unmet demand for product p of customer k in period t, 8k 2 K; p 2 P; t 2 T

Xyxt Quantity of x processed in facility y in period t, 8y 2 F [ R; x 2 C [ P; t 2 T

Xywxt Quantity of x transported from facility y to facility w in period t, 8y;w 2 FD;V ;RD; Z : y 6¼ w; x 2 C [ P; t 2 T

YyEt 1; if facility y is opened in period t;

8y 2 F [ V [ R; t 2 T

0; otherwise

8<

:

Yyt 1; if facility y is open in period t;

8y 2 F [ V [ R; t 2 T

0; otherwise

8<

:

YCCapUyt 1; if capacity of facility y is increased in

period t; 8y 2 F [ V [ R; t 2 T

0; otherwise

8<

:

24 of 23 Logist. Res. (2016) 9:24

123

Table 3 Definition of relevant parameters

Parameters Definition

a Discount rate

acp Number of component c yielded by the remanufacturing of one product unit of p, 8p 2 P; c 2 C

bcp Number of component c needed for producing one unit of product p, 8p 2 P; c 2 C

CapOyt Maximum capacity at facility y in period t (in m3), 8y 2 F [ V [ R; t 2 T

CapUy Minimum capacity at facility y (in m3), 8y 2 F [ V [ R

ccz Unit cost for procuring component c from supplier z, 8z 2 Z; c 2 C

cDEnt Disposal cost (per unit)

cUk Unit penalty cost for unmet demand k, 8k 2 K

cxyw Cost for transportation of a unit x from y to w (per km), 8y;w 2 F;V ;R;K : y 6¼ w; x 2 C [ P

cy Unit cost for processing at facility y, 8y 2 F [ R

dyx Time required for processing a unit of x at facility y, 8y 2 F [ V [ R; x 2 C [ P

e Size of capacity step by which the locations can be extended within one period (in m3)

fcapCostyCost for capacity increase at facility y by one step, 8y 2 F [ V [ R

fcapRevyRevenue for capacity reduction at facility y by one step, 8y 2 F [ V [ R

fy Cost for opening facility y, 8y 2 F [ V [ R

fyt Cost for open facility y in period t, 8y 2 F [ V [ R; t 2 T

gx Volume of one unit of x (in m3), 8x 2 C [ P

hcf Cost per period for holding a unit of c in inventory at plant f, 8f 2 F; c 2 C

hxr Cost per period for holding a unit of x in inventory at remanufacturing centre r, 8r 2 R; x 2 C [ P

LabCapOyt Maximum labour hours available at facility y in period t, 8y 2 F [ V [ R; t 2 T

LabCapUy Minimum labour hours at facility y, 8y 2 F [ V [ R

labccy Hourly cost for workforce at facility y, 8y 2 F [ V [ R

le Labour hours per worker per period

LT Last planning time period, LT 2 T

M Sufficiently large number

mdt Minimum proportion of returned products that has to be disposed after visual inspection at the DCCs in period t, 8t 2 T

mdct Minimum proportion of component c that has to be disposed after disassembly, remanufacturing and testing in period t,

8c 2 C; t 2 T

mr Minimum number of periods before products are returned for remanufacturing

Nkpt Demand of customer k for product p in period t, 8k 2 K; p 2 P; t 2 T

qtkpo Return rate in period t of customer k for product p, sold in period o, 8k 2 K; p 2 P; ðo; tÞ 2 T ; where o� t

sfy Cost for closing facility y, 8y 2 F [ V [ R

shxr Cost for disposing a stored unit of x at remanufacturing centre r at the end of the last planning, period LT, 8r 2 R; x 2 C [ P

shcf Cost for disposing a stored unit of c at facility f at the end of the last planning period LT, 8f 2 F; c 2 C

txyw Distance of y to w (in km), 8y;w 2 F;V ;R;K : y 6¼ w; x 2 C [ P

Logist. Res. (2016) 9:24 of 23 24

123

The discounted total costs are described by the follow-

ing objective function (1). For the sake of clarity the

objective function is split up into three different cost

functions. The first cost function presents the costs induced

by multi-period facility location, the second function

includes the costs resulting from capacity planning, and the

costs of aggregate production planning are described by the

third function. Below the functions are introduced followed

by the respective explanations.

min OF ¼ OF1 þ OF2 þ OF3 ð1Þ

with

OF1 ¼X

t2T

��

1=ð1þ aÞt�

��X

r2Rfr � Yr

Et

þX

v2Vfv � Yv

Et þX

f2Fff � Yf

Et

þX

r2Rf rt � Yr

t þX

v2Vf vt � Yv

t þX

f2Ff ft � Yf

t

þX

r2Rsfr � Hr

t þX

v2Vsfv � Hv

t þX

f2Fsff � Hf

t

þX

z2Z; c2C; f2Fðcczf � tczf þ cczÞ � Xzf

ct

þX

r2R; c2C; f2Fccrf � tcrf � Xrf

ct

þX

f2F; v2V ; p2Pcpfv � t

pfv � Xfv

pt

þX

v2V ; k2K; p2Pcpvk � t

pvk � Xvk

pt þX

k2K; p2PcUk � Uk

pt

þX

v2V ; k2K; p2Pcpkv � t

pvk � Xkv

pt

þX

v2V ; r2R; p2Pcpvr � tpvr � Xvr

pt

þ cDEnt ��

X

v2V ; p2PXvDpt þ

X

r2R; c2CXrDct

�

þX

c2C;ðr;sÞ2R:r 6¼s

ccrs � tcrs � EXIrsct

þX

p2P;ðr;sÞ2R:r 6¼s

cprs � tprs � EXIrspt

þX

c2C;ðf ;iÞ2F:f 6¼i

ccfi � tcfi � EXIfict

þX

p2P;ðv;jÞ2V:v 6¼j

cpvj � t

pvj � EXIvjpt

�

In themulti-period FLP studied in thiswork, the facilities can

be opened in one period and in the later periods they can stay

open or are closed. The variables YyEt, Y

yt andH

yt describe the

respective state of a facility. The costs for opening, i.e.

building, a facility, occur just once and are listed in line one

and two. For every period in which a facility remains open it

induces costs; these costs are captured by the terms in line

three. In line four the costs for closing a facility are stated.

The cost terms in the next line are for procuring and

shipping components from suppliers to plants. Costs for

transporting components from remanufacturing centres to

plants are listed in line six.

The transportation costs of the forward product flow, the

flow of products from plants to DCCs and from DCCs to

customers, and the penalty costs for unsatisfied demand are

stated in line seven and eight.

The cost terms in line nine and ten are the shipping costs of

the reverse product flow, i.e. the flow of products which are

returned by customers to DCCs and flow further in the net-

work to remanufacturing centres or to the disposal unit. In the

latter case, costs for disposing occur. The disposal costs for

returned products and remanufactured components are listed

in line eleven. The costs for distributing products or com-

ponents, respectively, on the same facility level are listed in

line 12–15.

OF2 ¼X

t2T

��

1=ð1þ aÞt�

��X

r2RfcapCostr � CCapUr

t

þX

f2FfcapCostf � CCapUf

t þX

v2VfcapCostv � CCapUv

t

þX

r2RfcapRevr � CCapDr

t þX

f2FfcapRevf � CCapDf

t

þX

v2VfcapRevv � CCapDv

t

�

At facilities, certain volume capacities inm3 are available and

they can be increased or decreased within one period. These

adjustments induce costs or revenues, as reflected by the cost

terms in line 1 and 2 or revenues in line 3 and 4, respectively.

OF3 ¼X

t2T

��

1=ð1þ aÞt�

��

X

r2R; c2Ccr � Xr

ct

þX

f2F; p2Pcf � Xf

pt þ le ��X

r2RlabccCostr � LCaprt

þX

f2FlabccCostf � LCapft þ

X

v2VlabccCostv � LCapvt

�

þX

r2R; p2Phpr � Irpt þ

X

r2R; c2Chcr � Irct

þX

f2F; c2Chcf � Ifct

�

þ ð1=ð1þ aÞLTÞ ��

X

f2F; c2Cshcf � EIfc

þX

r2R; p2Pshpr � EIrp þ

X

r2R; c2Cshcr � EIrc

�

24 of 23 Logist. Res. (2016) 9:24

123

Remanufacturing components at remanufacturing centres

and assembling products at plants induces costs, see lines

one and two. Labour hours of the workforce are needed for

performing the respective operations at the facilities. The

respective costs occur in every period and are stated in line

2 and 3.

Holding products and components at remanufacturing

centres and holding components at plants induces costs,

which are captured by the cost terms in lines 4 and 5.

The costs stated in lines 1–5 occur in every period,

and hence, these costs have to summed up over the

planning horizon. At the end of the planning horizon the

remaining items on stock at the facilities are disposed,

and the respective cost terms are stated in the last two

lines.

In the following, the constraints of the problem are

presented, but before that, important variables are

explained.

The variables YyEt, Y

yt and H

yt are interrelated. If a facility

is opened in one period, then it is running in this period;

therefore, both variables YyEt and Y

yt take value 1 and H

yt is

zero.

In the next period this facility can be still open, then

Yytþ1 ¼ 1 and Y

yEtþ1 ¼ 0, because the facility is already

opened, and Hytþ1 ¼ 0. However, the open facility can be

closed in t þ 1, then Hytþ1 takes value 1, and

Yytþ1 ¼ Y

yEtþ1 ¼ 0.

It is assumed that a facility cannot be opened again after

it is closed. The constraints (2)–(6) define these

interrelations.X

t2TYyEt � 1 8y 2 F [ R [ V ð2Þ

A facility can be opened just once in the planning horizon.

YyE1 ¼ Y

y1 8y 2 F [ R [ V ð3Þ

If a facility is opened in the first planing period, it is open

in period 1.X

t2T :t� s

ðYyEt � Hy

t Þ ¼ Yys

8y 2 F [ R [ V ; s 2 T : s[ 1

ð4Þ

If a facility is opened and not closed in one of the periods

t� s, where ðs; tÞ 2 T , then the facility is open in period s.

Yyt�1 � Yy

t �Hyt 8y 2 F [ R [ V ; t 2 T : t[ 1 ð5Þ

These constraints indicate the closing of facilities by

comparing the opening indicator variables of two succes-

sive periods.

X

t2THy

t � 1 8y 2 F [ R [ V ð6Þ

Closing of facilities is allowed to happen once within the

planning horizon.

The next set of constraints, constraints (7)–(19), describes

the forward and reverse product flows in the network and the

inventory balance at plants and remanufacturing centres.X

v2VXvkpt þ Uk

pt ¼ Nkpt 8k 2 K; p 2 P; t 2 T ð7Þ

Products are shipped from DCCs to satisfy demand of

customer k for product p in period t. Unsatisfied demand is

captured by Ukpt.

X

v2VXkvpt ¼ 0 8t 2 1; . . .;mr � 1f g; k 2 K; p 2 P ð8Þ

X

v2VXkvpt ¼

Xt

o¼1

�

qtkpo �X

v2VXvkpo

�

8t 2 mr; . . .; Tf g; k 2 K; p 2 P

ð9Þ

After mr periods, products can be returned for the first

time. In period t a proportion of products sold in period o,

qtkpo, is returned to DCCs. Every returned product is col-

lected in DCCs.

Ifct ¼ Ifct�1 þ

X

z2ZXzfct þ

X

r2RXrfct

þX

i2F:i 6¼f

EXIifct �X

i2F:i 6¼f

EXIfict � Xfct

8f 2 F; c 2 C; t 2 T : t[ 1

ð10Þ

These constraints represent the inventory balance equations

for components at plants.

Irpt ¼ Irpt�1 þX

v2VXvrpt þ

X

s2R:s6¼r

EXIsrpt

�X

s2R:s6¼r

EXIrspt � Xrpt

8r 2 R; p 2 P; t 2 T : t[ 1

ð11Þ

The inventory balance equations for returned products at

remanufacturing centres are stated in (11).

Irct ¼ Irct�1 þ Xrct þ

X

s2R:s6¼r

EXIsrct

�X

s2R:s 6¼r

EXIrsct �X

f2FXrfct

8r 2 R; c 2 C; t 2 T : t[ 1

ð12Þ

Components can be stocked at remanufacturing centres, too.

The inventory balance is determined by the equations (12).

Logist. Res. (2016) 9:24 of 23 24

123

Ifc1 ¼

X

z2ZXzfc1 þ

X

r2RXrfc1 þ

X

i2F:i 6¼f

EXIifc1

�X

i2F:i6¼f

EXIfic1 � X

fc1 8f 2 F; c 2 C

ð13Þ

Irx1 ¼ Xrx1 þ

X

s2R:s 6¼r

EXIsrx1 �X

s2R:s 6¼r

EXIrsx1

�X

f2FXrfx1 8r 2 R; x 2 C [ P

ð14Þ

The constraints (13) and (14) define the balance of the

respective inventory at the end of the first period.

IfcLT ¼ EIfc 8f 2 F; c 2 C ð15Þ

IrxLT ¼ EIrx 8r 2 R; x 2 C [ P ð16Þ

Products and components remaining in the respective

inventories at the end of the last planning period, LT, are

captured by (15) and (16).X

f2FXfvpt þ

X

j2V:j6¼v

EXIjvpt �X

j2V :j 6¼v

EXIvjpt

¼X

k2KXvkpt 8v 2 V ; t 2 T ; p 2 P

ð17Þ

Since no inventory at DCCs is allowed, every product

entering a DCC in period t also has to leave it in period t.X

v2VXfvpt ¼ Xf

pt 8f 2 F; t 2 T; p 2 P ð18Þ

There is no product inventory at plants, i.e. every assem-

bled product in a plant in period t is shipped to DCCs in the

same period.X

r2RDXvrpt ¼

X

k2KXkvpt 8v 2 V ; t 2 T ; p 2 P ð19Þ

Every returned product is shipped from DCCs either to

remanufacturing centres or to the disposal unit D.

The constraints (20) and (21) define the disposal quan-

tities in the network.

XvDpt �mdt �

X

k2KXkvpt 8v 2 V ; t 2 T; p 2 P ð20Þ

At least a proportion of mdt of the returned products has to

be disposed in period t, because of failing the inspection at

the DCCs.

mdct � Xrct �XrD

ct 8r 2 R; t 2 T ; c 2 C ð21Þ

After remanufacturing, at least a proportion of mdct of the

components does not comply with the requirements for as-

new components and is disposed.

The following constraint sets, the constraints (22)

and (23), describe the disassembly and assembly

operations at the remanufacturing centres and plants,

respectively.

Xrct ¼

X

p2Pacp � Xr

pt 8r 2 R; t 2 T; c 2 C ð22Þ

The number of as-new components, derived by disassem-

bling returned products and remanufacturing the respective

components, is defined by the equations above.

Xfct ¼

X

p2Pbcp � Xf

pt 8f 2 F; t 2 T; c 2 C ð23Þ

The number of components required for product assembly

at plants is defined by these equations.

At facilities capacity in labour hours and volume are

considered and have to be planned over the planning

horizon. The next sets of constraints, the constraints (24)–

(43), describe the capacity planning.

X

p2PdVp �

X

k2KðXkv

pt þ Xvkpt Þ

!

� le � LCapvt

8v 2 V; t 2 T

ð24Þ

The capacity level in terms of labour hours at facilities is

the product of one worker’s labour hours per period, le,

multiplied by the workforce available in t, determined by

LCapvt for DCCs. The constraints above adhere that the

labour hours needed for handling products at DCCs do not

exceed the available capacity level.X

c2CdRc � Xr

ct � le � LCaprt 8r 2 R; t 2 T ð25Þ

The labour hours used for remanufacturing at a remanufac-

turing centre cannot exceed the respective available capacity.X

p2PdFp � Xf

pt � le � LCapft 8f 2 F; t 2 T ð26Þ

At plants, capacity in terms of labour hours is needed for

assembling products. It is limited by the capacity level at a

plant.

LabCapUy � Yyt � le � LCapyt � LabCapOyt � Yy

t

8y 2 F [ V [ R; t 2 Tð27Þ

The capacity in labour hours at an open facility is restricted

by upper and lower bounds, forced by operations and the

availability of workers.X

c2Cgc � Ifct � e � Capft 8f 2 F; t 2 T ð28Þ

24 of 23 Logist. Res. (2016) 9:24

123

The volume capacity at the facilities is a multiple of e. The

volume of components stocked at an open plant cannot

exceed its available volume capacity.X

c2Cgc � Irct þ

X

p2Pgp � Irpt � e � Caprt 8r 2 R; t 2 T

ð29Þ

At an open remanufacturing centre, the volume of stored

products and components has to comply with the volume

capacity.

X

c2Cgc �

X

z2ZXzfct þ

X

r2RXrfct þ

X

i2F:i 6¼f

EXIifct

!

� e � Capft 8f 2 F; t 2 T

ð30Þ

The volume of components flowing into a plant is restricted

by the available volume capacity.X

p2Pgp � Xfv

pt � e � Capft 8f 2 F; t 2 T ð31Þ

The product flow through a plant adheres to the volume

capacity restriction of a plant.

X

c2Cgc � Xr

ct þX

s2R:s 6¼r

EXIsrct

!

þX

p2Pgp�

X

v2VXvrpt þ

X

s2R:s 6¼r

EXIsrpt

!

� e � Caprt

8r 2 R; t 2 T

ð32Þ

The volume of the components and products flowing into a

remanufacturing centre is limited by its volume capacity

restriction.

X

c2Cgc � Xrf

ct þX

s2R:s 6¼r

EXIrsct

!

þX

p2Pgp�

X

s2R:s 6¼r

EXIrspt

!

� e � Caprt

8r 2 R; t 2 T

ð33Þ

The volume of the components and products leaving a

remanufacturing centre has to be less or equal than the

respective capacity level.

X

p2Pgp �

X

f2FXfvpt þ

X

k2KXkvpt þ

X

j2V :j 6¼v

EXIjvpt

!

� e � Capvt 8v 2 V; t 2 T

ð34Þ

The volume of products flowing through a DCC has to

comply with its capacity.

CapUy � Yyt � e � Capyt �CapOyt � Yy

t

8y 2 F [ V [ R; t 2 Tð35Þ

The volume capacity level of a facility is a multiple of

e and is limited by given upper and lower bound.

Capyt � Capyt�1 ¼ CCapyt

8y 2 F [ V [ R; t 2 T : t[ 1ð36Þ

Volume capacity at facilities can be expanded or reduced

within one period.

Capy1 ¼ CCap

y1 8y 2 F [ V [ R ð37Þ

In the first planning period, the number of capacity steps at

a facility is identical to the capacity expansion carried out

in period 1.

CCapyt �CapOyt � YCCapUyt

8y 2 F [ V [ R; t 2 Tð38Þ

The variable YCCapUyt takes value 1, if the respective

variable CCapyt is bigger than zero, i.e. the capacity of

facility y is increased in period t.

CCapyt � CCapUyt �CapOyt � ð1� YCCapUy

t Þ8y 2 F [ V [ R; t 2 T

ð39Þ

Capacity increase is assigned to the variable CCapUyt .

CCapUyt �CapOyt � YCCapUy

t

8y 2 F [ V [ R; t 2 Tð40Þ

The upper capacity bound of a facility limits the capacity

increase.

CCapyt � CCapDyt �CapOyt � YCCapUy

t

8y 2 F [ V [ R; t 2 Tð41Þ

The variable CCapDyt captures the capacity decrease.

CCapDyt � � CapOyt � ð1� YCCapUy

t Þ8y 2 F [ V [ R; t 2 T

ð42Þ

Capacity decrease at a facility cannot be higher than the

respective upper capacity bound.

YCCapUyt � Yy

t 8y 2 F [ V [ R; t 2 T ð43Þ

Capacity can just be increased at an open facility.

Logist. Res. (2016) 9:24 of 23 24

123

Ukpt;X

kvpt ;X

vkpt ;X

vrpt ;X

zfct ;X

rct;X

rpt;X

rfct ;X

fvpt;

Xfpt;X

fct;EXI

rsct ;EXI

rspt ;EXI

fict;EXI

vjpt; I

fct; I

rct;

Irpt;EIfc ;EI

rc;EI

rp;Cap

rt ;Cap

ft ;Cap

vt ;CCapU

yt ;

LCaprt ; LCapft ; LCap

vt 2 Zþ 8p 2 P; c 2 C;

r 2 RD; k 2 K; v 2 V ; f 2 FD; z 2 Z; t 2 T

ð44Þ

Unsatisfied demand, the flows of products or components

between different echelons and between facilities of one

echelon, the produced units, the units on stock, the

capacities at the facilities and the capacity increase are

described by positive integer variables.

CCapyt 2 Z 8y 2 F [ V [ R; t 2 T ð45Þ

Variables describing the change of capacities at facilities

are integers and can be positive or negative.

CCapDyt 2 Z� 8y 2 F [ V [ R; t 2 T ð46Þ

The variables that determine the volume capacity decrease

are negative integer variables.

Yy; Yyt ;H

yt ; YCCapU

yt 2 0; 1f g

8y 2 F [ V [ R; t 2 Tð47Þ

Binary variables indicate the opening and closing of

facilities and the capacity increase.

5 Numerical analysis

In this section, the previously stated FLCAPPR model is

solved for an example data set. At first, the example, its

data and the solution are described, and then, the sensitivity

of the network to changes in the data is studied. The

influence of the cost parameters on the decision to

remanufacture is explored. Furthermore, the robustness of

the solution with respect to the quantity of returned prod-

ucts and the length of the planning horizon is examined by

varying the return rate and the number of periods in the

planning horizon. Selected interesting results are discussed.

5.1 Initial setting and solution

In the copier industry, CLSCNs as the one described in

Sect. 3 can be found. At copier manufacturer Xerox, for

example, ’’remanufactured parts are put onto the assembly

line for reuse in brand new copiers’’ [17]. Fleischmann et al

[8] study the facility location problem in a CLSCN of a

European copier remanufacturer for a single-period plan-

ning horizon.

In this paper a CLSCN for the copier industry in Ger-

many is to be designed. The product demand is assumed to

be bundled in the fifteen biggest German cities. As in [8]

the total product demand is assumed as 10 units per 1000

inhabitants, where the number of inhabitants is taken from

[29]. Furthermore, it is assumed that demand occurs in

every period of the planning horizon, since, as in [8], one

planning period equates to one year.

Costumers demand two different product types, P1 and

P2. Demand for P1 and P2 is assumed as equally high, i.e.

500 units of P1 and P2 are required, in every period.

It is possible to open DCCs and remanufacturing centres

at the demand locations. Suppliers and possible plant

locations are to be found only in the five biggest German

cities. In Fig. 2 the customer locations with their demand in

product units per planning period are given. Furthermore,

the suppliers and all possible locations for DCCs, reman-

ufacturing centres and plants are shown.

In the initial example used in this work, it is assumed

that demand for P1- and P2-products is known for five

years and remains constant over the planning horizon.

Later on, a sensitivity analysis is presented which includes

a study on the impact of varying the length of the planning

horizon.

The assembly of each product type requires one specific

component, M1 for P1- and M3 for P2-products, and one

component, M2, which is commonly used for both product

types. For simplicity the disassembly process is assumed to

be the reverse of the assembly process.

Fig. 2 Possible facility locations and the location of suppliers and

customers with their respective demand

24 of 23 Logist. Res. (2016) 9:24

123

The return rate qtkps, where ðs; tÞ 2 T : s� t, is inde-

pendent of customer location and product type, as in [8].

The multi-period modelling framework of the FLCAPPR

model allows to model a temporal shift between the for-

ward and reverse product flows in the network of t � s ¼mr periods, i.e. a residence time of a product with a cus-

tomer can be defined. In this work a residence time of one

year is assumed. Moreover, following [8] the return frac-

tion is assumed to be 50%, i.e. in the initial setting in this

work, 50% of products shipped to the customers are

returned at the beginning of the following period. There-

fore, for 5 planning periods the return rate is

q1kp1 ¼ q3kp1 ¼ q4kp1 ¼ q5kp1 ¼ q2kp2 ¼ q4kp2 ¼ q5kp2 ¼ q3kp3

¼ q5kp3 ¼ q4kp4 ¼ q5kp5 ¼ 0

and q2kp1 ¼ q3kp2 ¼ q4kp3 ¼ q5kp4 ¼ 0:5.

The other relevant parameters of the initial example and

their values can be found in Table 4. The fraction of the

returned products that has to be disposed, i.e. leaving the

network, is 0.6, as stated in [8]. However, in the CLSCN

studied in this work, returned products and components can

be disposed; therefore, here the sum of the fractions of

returned products md and components mdc that has to be

disposed is set to 0.6, i.e. md ¼ mdc ¼ 0:3. The trans-

portation costs in the network cpvk, c

pkv, c

pvr, c

crf , c

czf and c

pfv

are taken from [8]. It is assumed that the costs for shipping

goods between facilities of the same type are identical; the

distances between the locations are taken from [10].

The cost difference between the procurement costs cczand remanufacturing costs cr is assumed as 10 MU per

component, as described in [8]. Disposal costs cDEnt and

shxy; 8y 2 F [ R; x 2 C [ P are taken from [8] as well.

Following Silver’s [27] recommendations the inventory

holding costs hpr ¼ hcr ¼ hcf ; 8p 2 P; r 2 R; c 2 C; f 2 F are

assumed as 0.25 MU per unit per year.

The opening costs for the facilities, fv, ff and fr; are

taken from [8]. The costs and revenues for capacity

adjustments are based on these costs and assumed as

fcapCosty ¼ fcapRevy ¼ 1000 MU. This assumption is dis-

cussed in the following sensitivity analysis.

The volume capacity can be adjusted in steps of 1000

units. The lower volume capacity limits at facilities are

1000 m3; an open facility has to be equipped at least with

one volume capacity step. The capacity upper bound is

chosen such that one open DCC, remanufacturing centre

and plant is sufficient for the total product or component

flow, respectively.

It is assumed that capacity in labour hours can be

increased or decreased, respectively, by multiples of 1610

h. This results from the following calculation: in Germany

contractual labour hours per week often are 35 h. The

holiday entitlement is six weeks per calendar year.

Therefore, the number of labour hours of one worker per

year is ð52� 6Þ (’’working’’ weeks in a year) � 35 (hours

per week) ¼ 1610 (hours per year), neglecting public

holidays and downtime due to sickness.

The FLCAPPR problem with the described data setting

can be solved by the optimization software Gurobi 6.5.0 on

a two 3.10 GHz Intel Xeon Processor E5-2687W and 128

GB RAM computer in 197.71 seconds. The total dis-

counted costs are 19,534,389.05 MU.

In the solution, only one DCC and one plant are used;

both are located in Berlin and are open during the total

planning horizon. The open facilities and their capacity

equipments in the planning periods can be found in Fig. 3.

In every planning period products are shipped from the

open DCC in Berlin to the customers to meet their demand.

The products at the DCC originate from the plant in Berlin,

where these product quantities are assembled in every

period using components that are delivered from the sup-

plier in Berlin. In Fig. 4 the product and component flows

in the network are depicted.

The workforce and volume capacity at the open plant is

at the same level for every period, see Fig. 3, because in

every planning period the same amount of products and

components, respectively, are processed at the plant.

Since in the second period customers start to return

products at the DCC in Berlin, the workforce and volume

capacity at the DCC is increased from the first to the second

period, see Fig. 3. The customer demand and the amount of

products which are returned by customers remain the same in

the following periods, therefore, the workforce and volume

capacity at the DCC stay at the same level for the remaining

periods of the planning horizon.

Every returned product is collected in the DCC in Berlin

and then disposed. There is no open remanufacturing centre

in the network and no component remanufacturing takes

place in any period.

It is difficult to compare the results of the initial example

with previous studies of FLPs with reverse product flows,

e.g. in [8], since the planning problem is extended in this

work. Hence, additional parameters had to be introduced

and, therefore, the planning problems differ.

However, it is to be noticed that the solution of the

single-period facility location model presented in [8] rec-

ommends to open remanufacturing locations and that

recovered products should be used to meet demand, which

is different from the solution of the initial example of the

FLCAPPR problem in this work. Due to the fact that in the

multi-period approach taken here costs for volume capacity

Logist. Res. (2016) 9:24 of 23 24

123

Table 4 Definition of parameter data

Parameter Value

a 0.01

CapOyt 500,000 m3, 8y 2 F [ R; t 2 T

CapOvt 800,000 m3, 8v 2 V ; t 2 T

CapUy 1000 m3, 8y 2 F [ R [ V ; t 2 T

ccz 10 MU per component, 8c 2 C; z 2 Z

cDEnt 2.5 MU per unit

cUk 1000 MU per unit, 8k 2 K

ccyw 0.0030 MU per km, 8c 2 C; y 2 Z [ R; w 2 F

cpvk

0.01 MU per km, 8p 2 P; v 2 V ; k 2 K

cpkv

0.005 MU per km, 8p 2 P; v 2 V ; k 2 K

cpvr 0.003 MU per km, 8p 2 P; v 2 V ; r 2 R

cpfv

0.0045 MU per km, 8p 2 P; v 2 V ; f 2 F

cf 1 MU per unit, 8f 2 F

cr 0 MU per unit, 8r 2 R

dVp 0.5 h, 8p 2 P

dRc 2 h, 8c 2 C

dFp 1 h, 8p 2 P

e 1000 m3

fcapCosty1000 MU, 8y 2 F [ V [ R

fcapRevy1000 MU, 8y 2 F [ V [ R

fr 500,000 MU, 8r 2 R

ff 5,000,000 MU, 8f 2 F

fv 1,500,000 MU, 8v 2 V

fyt 10,000 MU, 8y 2 F [ V [ R; t 2 T

gp 10 m3, 8p 2 P

gc 2 m3, 8c 2 C

hxr 0.25 MU per unit, 8x 2 C [ P; r 2 R

hcf 0.25 MU per unit, 8c 2 C; f 2 F

LabCapOyt 1,000,000 h, 8y 2 F [ V [ R; t 2 T

labccy 15 MU per hour, 8y 2 F [ V [ R

le 1610 h

md 0.3

mdc 0.3, 8c 2 C

mr 1

sfy 50,000 MU, 8y 2 F [ V [ R

shxy 2.5 MU per unit, 8y 2 F [ R; x 2 C [ P

24 of 23 Logist. Res. (2016) 9:24

123

and workforce are included which were not considered in

[8] remanufacturing becomes less attractive and according

to the FLCAPPR model, opening a remanufacturing centre

and remanufacturing components is not cost-optimal.

5.2 Sensitivity analysis

In this section the sensitivity of the network structure to

changes in the data is studied. First, the impact of the cost

parameters on the decision to remanufacture is examined.

Then the effect of the return rate on the network design is

studied. Thereafter, the length of the planning horizon is

varied and the influence on the network design and espe-

cially on the remanufacturing decision is discussed.

Due to rather extensive computing times the following

tests were implemented allowing an optimality gap of up to

0:01%. The exceptional cases are marked.

5.2.1 Influence of cost parameters

By extending the FLP to a multi-period planning problem

in which facility locations, capacities and aggregate pro-

duction are optimized, additional cost parameters are

introduced in the objective function. In this section the

impact of these cost parameters on the decision to reman-

ufacture is studied.

Therefore, in the following fcapCostr ; labccr; frt and cr;

8r 2 R; t 2 T , i.e. the cost parameters for volume capacity

and labour hours at the remanufacturing centres, for open

remanufacturing centres and for remanufacturing, are var-

ied, and the results are discussed.

Influence of volume capacity cost parameters

In previous facility location models in networks with pro-

duct recovery, as i.e. in [8], the capacity level of a facility

is assumed as given and it is not cost-optimally determined.

Without taking into account costs for volume capacity,

over-capacities in the network can occur.

Furthermore, the capacity requirements resulting from

the flow of goods in a network with product recovery,

especially the increased capacity requirements induced by

the returned product flow additional to the requirements of

forward product flows, are not considered as costs in the

decision problem. In the FLCAPPR model building up

volume capacity at a remanufacturing centre leads to costs;

it is weighted with fcapCostr ; 8r 2 R, in the objective

function.

In the initial example this cost is assumed as 1000 MU.

Since in the solution of the initial example it is cost-opti-

mal to dispose returned products and procure all compo-

nents from a supplier, now the capacity cost is decreased to

study if it has an impact on the remanufacturing decision.

The solution of the initial example stays optimal until

fcapCostr ¼ 400; 8r 2 R. When fcapCostr � 400 MU, no rea-

sonable solutions are obtained. Now, it is optimal to open

every remanufacturing centre in periods 2–5, and volume

capacity is built up in one period and removed in the

•B

Open DCC in every period Open plant inevery period

t CapV1 463,000 m³2 695,000 m³3 695,000 m³4 695,000 m³5 695,000 m³

t CapF1 463,000 m³2 463,000 m³3 463,000 m³4 463,000 m³5 463,000 m³

t LabCapV1 24,150 hours2 35,420 hours3 35,420 hours4 35,420 hours5 35,420 hourst LabCapF1 46,690 hours2 46,690 hours3 46,690 hours4 46,690 hours5 46,690 hours

Fig. 3 Open facilities with their capacity levels

•

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•

Open DCC

Open plant

DD

B

HH

HB

H

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N

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S

•

Foward and reverse product flow

Component flow

Fig. 4 Product and component flows in the network

Logist. Res. (2016) 9:24 of 23 24

123

following period again and again over the planning horizon

to gain the revenues from the volume capacity decrease,

since fcapRevr ¼ 1000[ 400 ¼ fcapCostr . No returned prod-

ucts are processed at any remanufacturing centre. This

solution is hardly realistic and shows that the parameters

fcapCostr and fcapRevr have to be carefully determined.

Decreasing both parameters fcapCostr and fcapRevr down

to zero has no influence on the network, especially it

remains optimal to dispose every returned product instead

of opening remanufacturing centres and processing

returned products.

Influence of labour hour cost parameter

In previous studies, as in [8], the workforce at facilities

necessary for the respective operations at the facilities is

not considered. However, the decisions to open a reman-

ufacturing centre and to remanufacture components are

interrelated. For remanufacturing, workforce at a remanu-

facturing centre is needed whose labour hours cost money.

In this work, the workforce at facilities induces costs that

are taken into account in the objective function.

It is assumed that a labour hour at the remanufacturing

centre costs labccr ¼ 15 MU, 8r 2 R. The impact of this

cost parameter on the decision to remanufacture is studied

in the following.

It turns out that for every value of labccr [ 0 the

solution of the initial example remains cost-optimal.

However, setting this parameter to zero has an impact on

the network design. Now, it is cost-optimal to open a

remanufacturing centre in the second period additional to

the DCC and the plant in Berlin; the remanufacturing

centre remains open for the remaining periods. The net-

work and the open location with the respective capacity

equipment are shown in Fig. 5.

The total discounted costs are 19,345,018.28 MU. With

no labour hour cost at the remanufacturing centre, returned

products are shipped to the remanufacturing centre. There

returned products are stored or disassembled, and suit-

able components are remanufactured and used for product

assembly at the plant. The processed and stored quantities

are mapped in Figs. 6 and 7, respectively. In period 2-4 the

distribution quantities between the DCC and remanufac-

turing centre are the same, in the last period the reverse

product flow between the DCC and the remanufacturing

centre is lower: less P2-products are transported to the

remanufacturing centre. Since the quantity of products

returned from customers stays the same from the second to

the last period, the quantity of returned P2-products which

are disposed is increased and at the remanufacturing centre

less P2-products are disassembled in period 5. Therefore,

over the total planning period just 24.48% of the compo-

nents instead of the maximal possible 24.5% of the

components used at the plant for product assembly are

from the remanufacturing centre, the other components are

procured from the supplier in Berlin. (The maximum per-

centage results from the limited number of returned prod-

ucts, which in turn results from the return rate.)

The workforce at the remanufacturing centre is set at the

highest possible level in the second until the last period, see

Fig. 8, because workforce induces no labour hour costs

(labccr ¼ 0).

The volume capacity at the remanufacturing centre is

determined cost-optimally at 227,000 m3 for the second

until the fourth period. In the last planning period the

capacity is reduced by one step, thus 1000 m3, to obtain

revenues for capacity reduction. To comply with this

reduced volume capacity the returned product quantity

shipped to the remanufacturing centre is slightly decreased,

as the processed quantities at the remanufacturing centre,

see Fig. 6. Hence, the decisions regarding the volume

capacity level and the processed quantities at the remanu-

facturing centre and the reverse product flows in the net-

work are interrelated.

The capacity equipments of the plant and the DCC in

Berlin stay at the same levels as in the initial example,

because the product flows between the plant and the DCC

and between the DCC and the customers are not influenced

by the labour hour costs at the remanufacturing centre.

Furthermore, if a remanufacturing centre is opened, this

•

•

•

•

•

•

•

•

•

•

•

•

•

•

Open remanufacturingcentre in period 2-5Open DCC Open Plant

DD

B

HH

HB

H

L

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DU

D

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N

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Foward and reverse product flowReverse product flowComponent flow

Fig. 5 Network with no labour hour costs for remanufacturing,

labccr ¼ 0; 8r 2 R

24 of 23 Logist. Res. (2016) 9:24

123

does not have an impact on the DCC and plant location nor

on their capacity equipment.

Influence of costs for open remanufacturing centres

The FLCAPPR model optimizes the CLSCN over multiple

periods. It is assumed that a facility in this network can be

opened in any period and in the later periods the open

facility can be closed or stay open.

The opening costs are taken from [8] and the cost per

period for an open remanufacturing centre,

f rt ; 8r 2 R; t 2 T , are assumed in the initial example as

10,000 MU. In the initial example no remanufacturing

centre is opened. To study if and how this cost influences

this decision, the cost is decreased until f rt ¼ 0.

At f rt ¼ 0 it is still not cost-optimal to open a remanu-

facturing centre. Hence, decreasing the cost parameter

f rt ; 8r 2 R; t 2 T has no impact on the decision to open a

remanufacturing centre under this data setting.

Influence of remanufacturing cost parameter

As in [8], the difference between the remanufacturing and

procurement costs cr; 8r 2 R and ccz ; 8c 2 C; z 2 Z,

respectively, is assumed as 10 MU, that is cr ¼ 0; 8r 2 R

and ccz ¼ 10 MU; 8c 2 C; z 2 Z. The solutions presented in

[8] recommend remanufacturing of copiers unlike the solu-

tion of the initial example in this work. In this section it is

studied, if and how the remanufacturing costs in relation to

the procurement costs influence the remanufacturing

decision.

The FLCAPPR problem is solved with different values

for cr; 8r 2 R. Since no remanufacturing takes place at

cr ¼ 0; 8r 2 R, just negative values of cr; 8r 2 R are

studied, i.e. remanufacturing a component is subsidized.

For every 0[ cr [ � 30 MU; 8r 2 R the solution

remains the same as described in the solution of the initial

example. From cr ¼ �30 MU; 8r 2 R it is cost-optimal to

remanufacture. Hence, a difference of 40 MU between the

remanufacturing and procurement costs is necessary in

order to make remanufactured components preferable to

procured components. Because costs for volume capacity

and workforce are included in the FLCAPPR model, this

difference has to be bigger than in other studies where

these costs are ignored, e.g. in [8]. At cr ¼ �30 MU ; 8r 2R a remanufacturing centre in Berlin is opened in the

second period and stays open in the remaining periods.

Like in the solution of the initial example a DCC and a

plant in Berlin are open in every planning period. The

network and capacity levels at open facilities are mapped

in Fig. 9. The total discounted costs are 19,346,946.96 MU,

i.e. costs can be slightly decreased.

The capacity level and product flows between the plant

and the DCC and the DCC and the customers remain as in

2 3 4 5Disassembled P1-products 8096 8100 8100 8100Disassembled P2-products 8097 8100 8100 8043Remanufactured M1-components at plant 5667 5670 5670 5670

Remanufactured M2-components at plant 11335 11340 11340 11300

Remanufactured M3-components at plant 5667 5670 5666 5634

0

2000

4000

6000

8000

10000

12000

Period

Fig. 6 Processed quantities at remanufacturing centre,

labccr ¼ 0; 8r 2 R

2 3 4 5Stored returned P1-products 3 2 1 0Stored returned P2-products 2 1 0 0

0

1

2

3

Period

Fig. 7 Stored product quantities at remanufacturing centre,

labccr ¼ 0; 8r 2 R

Open remanu-facturing centrein period 2 - 5Open DCC in every period Open plant inevery period

t CapV1 463,000 m³2 695,000 m³3 695,000 m³4 695,000 m³5 695,000 m³

t CapF1 463,000 m³2 463,000 m³3 463,000 m³4 463,000 m³5 463,000 m³

t CapR2 227,000 m³3 227,000 m³4 227,000 m³5 226,000 m³


t LabCapR2 999,810 hours3 999,810 hours4 999,810 hours5 999,810 hours

B•

Fig. 8 Open facilities with their capacity levels for labccr ¼ 0; 8r 2 R

Logist. Res. (2016) 9:24 of 23 24

123

the solution of the initial example, see Fig. 4. However,

there is a product flow between the DCC and the reman-

ufacturing centre in Berlin, as shown in Fig. 5.

From the second until the last period products collected

at the DCC are shipped to the remanufacturing centre. At

the remanufacturing centre the returned products are stored

and disassembled to components and suitable components

are remanufactured. After remanufacturing, the compo-

nents are shipped to the plant. The processed and stored

quantities at the remanufacturing centre are mapped in

Figs. 10 and 11, respectively.

Every remanufacturable returned product and compo-

nent is processed at the remanufacturing centre and then

shipped from the remanufacturing centre to the plant, i.e.

there are no items on inventories at the end of period 5.

In addition to remanufactured components, components

have to be procured from the supplier in Berlin; only

24.5% of the components used in the product assembly are

remanufactured components. Compared to the solution of

the previous section for labccr ¼ 0; 8r 2 R, this fraction is

slightly increased. For cr ¼ �30; 8r 2 R every remanu-

facturable product is processed at the remanufacturing

centre.

There is an interrelation between the decisions to store

and process products and the capacity equipment at the

remanufacturing centre, as the capacity levels at the

remanufacturing centre are adapted to the requirements of

the processed and stored quantities, see Figs. 10 and 11. By

storing products from the second to the fourth period

instead of processing them immediately at the remanu-

facturing centre, less workforce is necessary at the

remanufacturing centre in these periods, see Fig. 9. How-

ever, due to building up inventory at the remanufacturing

centre from the second until the fourth period, more vol-

ume capacity is necessary in the fifth period; in the last

period the capacity has to be increased to comply with the

increased volume requirements. In the last planning period

all items on inventory are processed, therefore, the work-

force in the last period is increased, too, see Fig. 9.

5.2.2 Influence of return rate

The FLCAPPR model is solved with different values for

qtkps; 8 k 2 K; p 2 P; ðs; tÞ 2 T : s� t, i.e. with return rates

from 0 to 1, increasing in steps of 0.1. The respective total

discounted costs and selected decision variable values for

the results can be found in Fig. 12.

When there are no returned products at all, a plant and

DCC are opened in Berlin, but of course no remanufac-

turing centre is opened. The total discounted costs are

•B

Open remanu-facturing centrein period 2-5Open DCC in every period Open plant inevery period

t CapV1 463,000 m³2 695,000 m³3 695,000 m³4 695,000 m³5 695,000 m³

t CapF1 463,000 m³2 463,000 m³3 463,000 m³4 463,000 m³5 463,000 m³

t CapR2 227,000 m³3 227,000 m³4 227,000 m³5 228,000 m³


t LabCapR2 64,400 hours3 64,400 hours4 64,400 hours5 66,010 hours

Fig. 9 Network with negative remanufacturing costs,

cr ¼ �30; 8r 2 R

Fig. 10 Processed quantities at remanufacturing centre,

cr ¼ �30; 8r 2 R

2 3 4 5Stored returned P1-products 9 8 107 0Stored returned P2-products 89 188 187 0

0

50

100

150

200

Period

Fig. 11 Stored product quantities at remanufacturing centre,

cr ¼ �30; 8r 2 R

24 of 23 Logist. Res. (2016) 9:24

123

18, 266, 247.79 MU and, hence, lower than before, as no

transportation and other costs for returned products occur.

For every return rate from 0 to 1, the decision regarding

the opening and the capacity equipment of the plant

remains the same. Moreover, for every return rate no

remanufacturing centre is opened, every returned product is

disposed and every component used in the product

assembly is procured from the supplier in Berlin.

The total discounted costs of the CLSCN increase with

the return rate, see Fig. 12. This cost increase is induced by

higher capacity and by disposal and opening costs due to an

increased quantity of returned products which are collected

in the DCCs and disposed afterwards.

Due to the assumption that returned products have to be

collected at DCCs, the return rate has an influence on the

capacity equipment at the DCC and the opening decision

regarding DCCs, as every returned product flows through a

DCC and requires handling times and space, see Fig. 12.

For a return rate between 0.8 and 1 the volume capacity of

one DCC is not sufficient any more; therefore, a DCC in

Dortmund is opened additional to the DCC in Berlin. The

resulting network with the product and component flows is

displayed in Fig. 13.

From the DCC in Dortmund products are shipped to

customers in Dortmund, Duisberg, Dusseldorf, Essen,

Frankfurt am Main and Cologne in every planning period,

and in the first period the demand of customers in Stuttgart

is met by products from the DCC in Dortmund. The

remaining customers receive their products from the DCC

in Berlin.

Some reverse product flows are different from the for-

ward product flows. Customers in Bremen and Hannover

return their products to the DCC in Dortmund, although

they get products from the Berlin DCC. The other cus-

tomers return their products to the DCC which delivered

the product.

The results show that the reverse product flow influences

the forward product flow and the optimal network

structure, if the quantity of returned products is high, as in

[8]. Therefore, the forward and reverse product flows have

to be planned simultaneously in order to achieve an optimal

network.

Moreover, it turns out that a higher quantity of returned

products increases the total costs, but does not necessarily

result in a network with remanufacturing. There is no

return rate at which it is cost-optimal to open a remanu-

facturing centre and use remanufactured components in the

product assembly under the initial data setting, in particular

for the assumed cost parameters.

Now, it is examined which results occur when it is cost-

optimal to open a remanufacturing centre and to remanu-

facture all suitable components and the return rate is

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Labour Hours at DCCs in period 1 24150 24150 24150 24150 24150 24150 24150 24150 24150 24150 24150Labour Hours at DCCs in period 2-5 24150 25760 28980 30590 33810 35420 37030 40250 41860 45080 46690Capacity at DCCs in 1 in m3 463000 463000 463000 463000 463000 463000 463000 463000 463000 463000 463000Capacity at DCCs in 2 - 5 in m3 463000 510000 556000 602000 648000 695000 741000 787000 834000 880000 926000Sum of disposed returned products 0 18530 37024 55536 74048 92560 111072 129584 148096 166608 185120Total Cost in MU 18266248 18482777 18792549 19008088 19317860 19534389 19749928 20059700 21562548 21858757 22060733

01000002000003000004000005000006000007000008000009000001000000

0

5000000

10000000

15000000

20000000

25000000

Return rate

Fig. 12 Variation of return rate with cr ¼ 0; 8r 2 R

•

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•

•DD

B

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Foward Product flow

Component flow

Reverse product flow in period 1-5

Foward Product flowin period 1Foward Product flowin period 2-5

Fig. 13 Network with two DCCs for qtkps ¼ 0:8; 0:9; 1f g

Logist. Res. (2016) 9:24 of 23 24

123

varied. Therefore, the FLCAPPR model is solved with cr ¼�30; 8r 2 R and for return rates from 0 to 1, increasing in

steps of 0.1. The respective total discounted costs of the

resulting network and selected decision variable values for

the results can be seen in Fig. 14.

The total discounted costs increase with the return rate,

like in the study with cr ¼ 0; 8r 2 R. However, for cr ¼�30; 8r 2 R the cost increase for 0:4� qtkps � 1 is slightly

smaller, see Fig. 15.

At return rates qtkps\0:4, every returned product is

disposed and the network consists of a DCC and plant in

Berlin, as in the solution of the initial example. Unlike in

the study with cr ¼ 0, with cr ¼ �30 an increase of the

return rate has an impact on the decision to open a

remanufacturing centre and to remanufacture components.

For values of qtkps ¼ 0:4 to qtkps ¼ 1, a remanufacturing

centre in Berlin is opened in the second period which stays

open over the remaining planning periods. For these return

rates, the respective maximal possible amount of compo-

nents is remanufactured and used in the product assembly

instead of procured components. Because remanufactured

components are cheaper production inputs than procured

components, for these return rates the total cost increase in

the study with cr ¼ �30 is smaller than for the study with

cr ¼ 0 where no remanufacturing takes place, see Fig. 15.

For 0:4� qtkps � 0:7, it is cost-optimal to ship returned

products from the DCC in Berlin to the remanufacturing

centre in Berlin. The remanufactured components are used

in the product assembly in the plant in Berlin. The network

for these return rates was shown already in Fig. 5.

As can be seen in Fig. 14, the capacity level at the

remanufacturing centre increases with the return rate, i.e.

with the quantity of returned products. Over the planning

periods the capacity levels at the remanufacturing centre

can change, too. This happens when returned products are

stored and remanufactured in a later period, instead of

being remanufactured immediately.

The capacity levels at the DCC increase with the return

rate, too. At qtkps ¼ 0:8; 0:9; 1f g two DCCs, a DCC in

Berlin and Dortmund, have to be opened to have enough

capacity for the returned products, as in the study with

cr ¼ 0. The opening costs for the second DCC cause the

jump in the total costs, see Fig. 15. The location of the

remanufacturing centre and the plant stays at Berlin.

This analysis has shown that opening a remanufacturing

centre and using remanufactured components in the pro-

duct assembly is cost-optimal under specific remanufac-

turing costs and only if the return rate is high enough,

qtkps � 0:4. Moreover, high return rates, qtkps ¼ 0:8; 0:9; 1f g,influence the network design and the distribution system,

whether remanufacturing is cost-optimal or not.

5.2.3 Influence of the number of planning periods

In contrast to previous facility location models with reverse

product flows the FLCAPPR model optimizes the CLSCN

over multiple periods instead of a single period. A period is

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8* 0.9** 1***Labour Hours at rem. centre in 2 & 3 0 0 0 0 51520 64400 77280 90160 103040 115920 128800Labour Hours at rem. centre in 4 0 0 0 0 51520 64400 77280 91770 104650 117530 130410Labour Hours at rem. centre in 5 0 0 0 0 51520 66010 78890 90160 64400 74060 80500Capacity at rem. centre in 2 & 3 in m3 0 0 0 0 182000 227000 272000 317000 363000 408000 453000Capacity at rem. centre in 4 in m3 0 0 0 0 182000 227000 272000 319000 364000 410000 455000Capacity at rem. centre in 5 in m3 0 0 0 0 178000 228000 273000 316000 225000 258000 280000Sum of rem. components 0 0 0 0 72128 90708 108754 126786 131294 148198 163976Sum of disp. ret. products 0 18512 37024 55536 22528 27768 33390 39022 54314 60751 67993Solution times in seconds 33 2530 2211 1739 2486 1368 1833 1641 8634 418270 431468Total cost in MU 18266248 18482777 18792549 19008088 19274525 19346947 19417848 19581710 20991910 21149822 21214104

050000100000150000200000250000300000350000400000450000500000

0

5000000

10000000

15000000

20000000

25000000

Return Rate Interrupted at:* 0,09% ** 0,22% ***0,19%

Fig. 14 Variation of return rate with cr ¼ �30; 8r 2 R

0200000400000600000800000

1000000120000014000001600000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

MU

Return rate

Cost increase with cr = -30 Cost increase with cr = 0

Fig. 15 Cost increase by variation of return rate with cr ¼ 0; 8r 2 R

and cr ¼ �30; 8r 2 R

24 of 23 Logist. Res. (2016) 9:24

123

assumed as one year, and the length of the planning hori-

zon can be interpreted as the product life-cycle. In the

initial example the CLSCN is planned over 5 periods. In

this section, the impact of the length of the planning

horizon on the network is studied; therefore, the number of

periods is varied.

The total discounted costs, the satisfied product demand

and the disposed returned products over a planning horizon

of 2–7 periods are listed in Fig. 16.

It is assumed that demand and return rate remain the

same over the planning horizon. The structure of the

solution of the initial example remains optimal, i.e. the

network stays the same for an increased number of periods

in the planning horizon. Especially, the decision to procure

the components for the product assembly instead of

remanufacturing components stays the same for the dif-

ferent length of the planning horizon under this data

setting.

The capacity costs and the costs for open facilities rise when

the number of periods is increased. Moreover, since products

and components have to be transported, processed and pro-

cured, respectively, these costs increase with the number of

planning periods, too. Hence, the total discounted costs grow

when the planning periods are increased, see Fig. 16.

It is examined if the length of the planning horizon does

not influence the network design and the production and

stored quantities in the network, if remanufacturing is cost-

optimal. Therefore, the FLCAPPR model is solved with

cr ¼ �30; 8r 2 R for planning horizons of 2–7 periods.

The total discounted costs and selected interesting decision

variables are mapped in Fig. 17.

Increasing the planning horizon to six and seven periods

results in the same network as in the solution with 5

periods, which was already described above. In this solu-

tion, remanufacturing takes place at an open remanufac-

turing centre in Berlin, see Fig. 5.

Decreasing the planning horizon of 5 periods by just one

period, to 4 periods, changes the network design. Now, it is

cost-optimal to procure every component for the product

assembly from the supplier in Berlin instead of remanu-

facturing components. The resulting network is as in the

solution of the initial example, where only a DCC and plant

in Berlin are opened and both stay open over the planning

horizon.

765432Total satisfied product demand 92560 138840 185120 231400 277680 323960Total disposed returned products 23140 46280 69420 92560 115700 138840Solution times in seconds 700 340 493 198 343 846Total cost in MU 12320122 14748845 17153521 19534389 21891684 24225639

0

50000

100000

150000

200000

250000

300000

350000

0

5000000

10000000

15000000

20000000

25000000

30000000

Number of planning periods

Fig. 16 Variation of planning horizon length with cr ¼ 0; 8r 2 R

2 3 4 5 6 7Total satisfied product demand 92560 138840 185120 231400 277680 323960Total disposed returned products 23140 46280 69420 27768 34808 41838Solution times in seconds 10 646 729 1368 20529 4341Total rem.components used in assembly 0 0 0 90708 113248 135797Total cost in MU 12320122 14748845 17153521 19346947 21482068 23596497

0

50000

100000

150000

200000

250000

300000

350000

0

5000000

10000000

15000000

20000000

25000000

Number of planning periods

Fig. 17 Variation of planning horizon length with cr ¼ �30; 8r 2 R

Logist. Res. (2016) 9:24 of 23 24

123

Hence, the number of periods in the planning horizon

has an impact on the network design and the decision to

remanufacture. A multi-period planning approach in con-

trast to a single-period approach, as in [8], for a CLSCN is

useful and leads to new and different results. Therefore, the

relevant number of periods has to be determined and the

network has to be analysed over this planning horizon.

6 Conclusions and future research directions

In this work, the strategic CLSCN design is extended by

capacity and production planning on an aggregate level.

The resulting FLCAPPR model determines the cost-opti-

mal network design, the facility locations and capacity

equipment at open facilities, and the cost-optimal pro-

curement, production and distribution quantities in the

CLSCN over a finite planning horizon consisting of mul-

tiple periods. It is solved for an example from the copier

industry with input data based on previously published

research [8]. Furthermore, possible effects of the extended

planning approach on the network design, especially on the

decision to recover returned products, are studied in a

sensitivity analysis. Thereafter, the robustness of the net-

work design and the production and distribution quantities

regarding the return rate, i.e. the quantity of returned

products, is examined. In a further study the influence of

the planning horizon length is investigated.

Extending a single-period FLP to the FLCAPPR model

leads to new and different results concerning the decision

to remanufacture and the effect of the return rate on the

network. In contrast to a previous study [8], in this setting,

it is cost-optimal to dispose returned products instead of

recovering them and use the resulting components in the

product assembly based on the FLCAPPR model. When

capacity costs, especially labour hour costs at the reman-

ufacturing centre, are included, remanufacturing is cost-

optimal only if the remanufacturing costs are sufficiently

low compared to the procurement costs for new compo-

nents from suppliers. Hence, production costs, in particular

remanufacturing costs, have a large impact on facility

location and capacity equipment decisions. Furthermore,

the interdependence between the capacity equipment at the

remanufacturing centre and the procuring decision, the

processing and storing quantities at the remanufacturing

centre is determined. Hence, these decisions have to be

optimized jointly, as in the FLCAPPR model.

The decisions regarding facility locations and capacity

equipment are robust for low return rates. From return rates

of 40% remanufacturing takes place, if remanufacturing

costs are sufficiently low. Moreover, for high return rates,

rates of 80% and more, the facility location decisions and

the distribution system are changed compared to the results

for lower rates. Therefore, the forward and reverse product

flows in the network have to be planned together.

The multi-period setting of the FLCAPPR model

enables a study of the influence of the planning horizon on

the decision to remanufacture and provides new informa-

tion compared to single-period FLPs, as in [8]. Product

recovery is cost-optimal only if remanufacturing costs are

sufficiently low compared to procurement costs and the

planning horizon is sufficiently long. For the studied data

setting, this means that there has to be product demand for

at least 5 periods, i.e. five years; only then remanufacturing

can be cost-optimal.

Following the CLSC-Management definition in [12], a

CLSCN has to be studied over the total product life-cycle

with consideration of varying demand and returned product

quantities and qualities. Hence, in the future the FLCAPPR

problem should be solved with data sets consisting of

varying demand and returned product quantities in order to

study possible product life-cycle effects.

Moreover, when residence times are longer than one

period, the reverse product flow starts later in the planning

horizon. This can affect decisions regarding the facility

locations and capacity equipment and, therefore, the

remanufacturing decision. Hence, different assumptions

regarding the residence times of products should be

examined in the future.

Linear costs and revenues for adjusting capacity are

assumed here, and the effects of economies of scale and

learning effects gained by higher production quantities and

bigger facilities are not considered. Furthermore, the pos-

sibilities to increase or decrease labour hours at facilities by

overtime or part-time, respectively, is not modelled. These

aspects require further model extensions, but it has to be

noted that the FLCAPPR model is already large scale with

rather lengthy solving times.

Finally, uncertainties regarding the quantity and quality

of reverse product flows are an issue of CLSCM [11–13].

They are not considered here, because an APP framework

is used. However, other approaches integrating uncertain-

ties might be developed; this is left for future research.

Open Access This article is distributed under the terms of the

Creative Commons Attribution 4.0 International License (http://crea

tivecommons.org/licenses/by/4.0/), which permits unrestricted use,

distribution, and reproduction in any medium, provided you give

appropriate credit to the original author(s) and the source, provide a

link to the Creative Commons license, and indicate if changes were

made.

References

1. Akcali E, Cetinkaya S, Uster H (2009) Network design for

reverse and closed-loop supply chains: an annotated bibliography

of models and solution approaches. Networks 53:231–248

24 of 23 Logist. Res. (2016) 9:24

123

http://creativecommons.org/licenses/by/4.0/

http://creativecommons.org/licenses/by/4.0/

2. Akinc U, Khumawala BM (1977) An efficient branch and bound

algorithm for the capacitated warehouse location problem. Manag

Sci 23:585–594

3. Akinc U, Roodman GMA (1986) New approach to aggregate

production planning. IIE Trans 18:88–94

4. Bostel N, Dejax P, Lu Z (2005) The design, planning, and opti-

mization of reverse logistics networks, logistics systems: design

and optimization. Springer, New York, pp 171–212

5. Fleischmann B, Meyr H, Wagner M (2015) Advanced planning.

Supply chain management and advanced planning. Springer,

Berlin

6. Fleischmann M, Bloemhof-Ruwaard JM, Dekker R, van der Laan

E, van Nunen JAEE, Van Wassenhove LN (1997) Quantitative

models for reverse logistics: a review. Eur J Oper Res 103:1–17

7. Fleischmann M, Krikke HR, Dekker R, Flapper SDP (2000) A

characterisation of logistics networks for product recovery.

Omega 28:653–666

8. Fleischmann M, Beullens P, Bloemhof-Ruwaard JM, Van

Wassenhove LN (2001) The impact of product recovery on

logistics network design. Prod Oper Manag 10:156–173

9. Fleischmann M, Bloemhof-Ruwaard JM, Beullens P, Dekker R

(2004) Reverse logistics network design. Reverse logistics:

quantitative models for closed-loop supply chains. Springer,

Berlin

10. Google Maps: Google Maps. https://maps.google.com. Version:

2015, checked on: 12.01.2015

11. Guide VDR Jr (2000) Production planning and control for

remanufacturing: industry practice and research needs. J Oper

Manag 18:467–483

12. Guide VDR Jr (2009) The evolution of closed-loop supply chain

research. Oper Res 57:10–18

13. Guide VDR, Jayaraman V, Srivastava R (1999) Production

planning and control for remanufacturing: a state-of-the-art sur-

vey. Robot Comput Integr Manuf 15:221–230

14. Jayaraman V (1998) Transportation. Facility location and

inventory issues in distribution network design. Int J Oper Prod

Manag 18:471–494

15. Jayaraman V (1999) A closed-loop logistics model for remanu-

facturing. J Oper Res Soc 50:497–508

16. Jayaraman V (2006) Production planning for closed-loop supply

chains with product recovery and reuse: an analytical approach.

Int J Prod Res 44:981–998

17. King A, Miemczyk J, Bufton D (2006) Photocopier remanufac-

turing at Xerox UK. A description of the process and

consideration of future policy issues. Innovation in life cycle

engineering and sustainable development. Springer, Dordrecht

18. Lund RT (1998) Remanufacturing: an American resource.

International Congress Environmentally Conscious Design and

Manufacturing, Rochester

19. Marın A, Pelegrın B (1998) The return plant location problem:

modelling and resolution. Eur J Oper Res 104:375–392

20. Nam S, Logendran R (1992) Aggregate production planning—a

survey of models and methodologies. Eur J Oper Res 61:255–272

21. Perl J, Sirisoponsilp S (1988) Distribution networks: facility

location. Transportation and inventory. Int J Phys Distrib Mater

Manag 18:18–26

22. Pishvaee MS, Torabi SA (2010) A possibilistic programming

approach for closed-loop supply chain network design under

uncertainty. Fuzzy Sets Syst 161:2668–2683

23. Salema MIG, Barbosa-Povoa AP, Novais AQ (2007) An opti-

mization model for the design of a capacitated multi-product

reverse logistics network with uncertainty. Eur J Oper Res

179:1063–1077

24. Schultmann F, Engels B, Rentz O (2003) Closed-loop supply

chains for spent batteries. Interfaces 33:57–71

25. Schultmann F, Zumkeller M, Rentz O (2006) Modeling reverse

logistic tasks within closed-loop supply chains: an example from

the automotive industry. Eur J Oper Res 171:1033–1050

26. Shen ZM (2007) Integrated supply chain design models: a survey

and future research directions. J Ind Manag Optim 3:1–27

27. Silver EA (1967) A tutorial on production smoothing and work

force balancing. Oper Res 15:985–1010

28. Souza GC (2013) Closed-loop supply chains: a critical review,

and future research. Dec Sci 44:7–38

29. Statistische Amter des Bundes und der Lander: Gemeindeverze-

ichnis-Sonderveroffentlichung Gebietsstand: 31.12.2011 (Jahr):

Großstadte (mit mindestens 100 000 Einwohnerinnen und Ein-

wohnern) in Deutschland nach Bevolkerung am 31.12.2011 auf

Grundlage des Zensus 2011 und fruherer Zahlungen. https://

www.destatis.de/DE/ZahlenFakten/ LaenderRegionen/Re-

gionales/Gemeindeverzeichnis/ Administrativ/GrosstaedteEin-

wohner.html. Accessed on 01/15/2015

30. Steinke L, Fischer K (2015) Integrated facility location, capacity,

and production planning in a multi-commodity closed supply

chain network. Logistic management. Springer, Berlin

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